Georgian Court University 

Effective Graphing: Using Graphs to Present Data (Part 1)Grade Level: 68 Time Frame: 4045 minutes Subject: Math Introduction to Lesson: Almost all scientific and technical reports, as well as more "mainstream" media like newspapers and magazines, contain tables and figures. The purpose of these tables and figures is to display data and illustrate ideas and concepts in an organized fashion, so that it is easier for others to understand. There are many different types of graphs. Depending on the nature of the data, some graphs are more appropriate than others. Knowing the appropriate type of graph to use to illustrate a given data set is a crucial skill that students need to master. This and the subsequent lesson in the sequence will work with students to review / learn how to pick the appropriate kind of graph to display different kinds of data sets. Students then will practice creating different kinds of graphs using the data on the Phragmites invasion that they’ve collected in previous classes. NJ New Jersey Core Curriculum Content Standards STANDARD 4.1 (Number and numerical operations) All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways. A. Number Sense 1. Use reallife experiences, physical materials, and technology to construct meanings for numbers · Explore the use of ratios and proportions in a variety of situations. C. Estimation 1. Use a variety of strategies for estimating both quantities and the results of computations. 3. Determine the reasonableness of an answer by estimating the result of operations. 4. Determine whether a given estimate is an overestimate or an underestimate. STANDARD 4.2 (Geometry and measurement) All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena. D. Units of Measurement 5. Use measurements and estimates to describe and compare phenomena E. Measuring Geometric Objects 5. Develop informal ways of approximating the measures of familiar objects (e.g., use a grid to approximate the area of the bottom of one's foot). STANDARD 4.3 (Patterns and algebra) All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes. C. Modeling 2. Draw freehand sketches of graphs that model real phenomena and use such graphs to predict and interpret events. 1. Changes over time 2. Relations between quantities STANDARD 4.4 (Data analysis, probability, and discrete mathematics) All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data. A. Data Analysis (or Statistics) 1. Collect, generate, organize, and display data. 2. Read, interpret, select, construct, analyze, generate questions about, and draw inferences from displays of data. o Bar graph, line graph, circle graph, table, histogram o Range, median, and mean o Calculators and computers used to record and process information STANDARD 3.1 (Reading) All students will understand and apply the knowledge of sounds, letters, and words in written English to become independent and fluent readers, and will read a variety of materials and texts with fluency and comprehension. A. Concepts About Print/Text 1. Use a … glossary independently and appropriately. C. Decoding and Word Recognition3. Apply knowledge of new words correctly STANDARD 1.2 (Creation and Performance) All students will utilize those skills, media, methods, and technologies appropriate to each art form in the creation, performance, and presentation of dance, music, theater, and visual art. D. Visual Art 1. Individually or collaboratively create two and threedimensional works of art employing the elements and principles of art. 3. Recognize and use various media and materials to create different works of art Materials and Resources:
Objectives:
Vocabulary Continuous variable: when a variable can have any possible value (fractions, decimals etc.) within the scale of the measurement, then that variable is said to be continuous. If a variable is continuous, it is always possible to find an intermediate value between any two values on the scale e.g. Length, weight, nutrient concentration. Discrete variable: one which has specific values for which no meaningful intermediate exists. Discrete variables can be categorical (nominal) or ordinal. Categorical variables are those which exist in discrete units to which there is no obvious order (e.g. “male, female” or “red, blue, green”). Ordinal variables are still discrete but can be arranged a logical order (e.g. “poor, middle class, wealthy” or “private, sergeantmajor, general”). Graph: A diagram that provides a visual representation of a data set (sometimes also called chart or plot). X / Y Axis (plural = axes): In twodimensional plots the vertical scale is usually the yaxis, and the horizontal scale is the xaxisParts of a graph
Anticipatory Set: Teacher will provide the students with handouts with the vocabulary words and table with characters of the different graphs. If desired, review the vocabulary of graphing and information on types of graph with the students. Alternately, teacher can jump straight into playing the “categorical or continuous” and / or “What’s wrong with this picture?” games with students using the PowerPoint presentations provided and allow the students to “learn through application”. Sequence Instruction:
To keep students on task, a graphic organizer is provided that students can use to keep track of the different data sets, and note for each which the independent (X) and which was the dependent or measured variable (Y). Further, for each X variable the students will note which are continuous or categorical
Again, to keep students on task, a graphic organizer is provided that students can use to keep track of the graphs they look at, the errors they detected, the reason that the graphs were wrong and what they would need to do to present the data correctly.
Accommodations and Modification:
Assessment / Homework / Anchor Activity (if lesson goes shorter than planned) Have students complete similar graphs for data from the marsh at different stages in the invasion. Closure Each student will create a graph with a deliberate mistake (reversed axes, missing legends, wrong type of graph for the type of data being presented etc.). This graph could make use of data collected in previous classes or, alternately, the student could create a totally fictional data set. Once the graph is made, have students pair up and exchange graphs and challenge one another to find the error and write that error on the sketch / print out. Each student will then provide feedback to their partners (acknowledging and congratulating them on correctly diagnosing errors, providing hints if the error is not recognized by the partner). Students will turn in their graphs, and their partner’s diagnoses of the error(s) to the teacher as they leave for the day. Alternately, teacher could ask a lightning round of questions re: the vocabulary for the lesson (continuous, variable, etc.) (S)he could use graphs to ask the questions or refer to the ones the students have done.
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© 2009. Louise Wootton. Edited by Claire Gallagher Although the information in this document has been funded wholly or in part by the United States Environmental Protection Agency under assistance agreement NE97262206 to Georgian Court University, it has not gone through the Agency's publications review process and, therefore, may not necessarily reflect the views of the Agency and no official endorsement should be inferred.
